Compact minimal hypersurfaces of index one and the width of real projective spaces

TL;DR

This paper characterizes the minimal hypersurfaces of index one in real projective spaces, linking their width to Clifford hypersurfaces, and computes their Morse index in complex and quaternionic projective spaces.

Contribution

It provides a characterization of the first min-max width in real projective spaces and calculates the Morse index of Clifford hypersurfaces in complex and quaternionic cases.

Findings

Width of real projective spaces equals the area of Clifford hypersurfaces

Morse index of Clifford hypersurfaces in complex projective spaces is computed

Morse index of Clifford hypersurfaces in quaternionic projective spaces is computed

Abstract

We characterize the first min-max width of real projective spaces of any dimension. The width is the minimum area over the Clifford hypersurfaces. We also compute the Morse index of the Clifford hypersurfaces in the complex and quaternionic projective spaces.